Stability of Gasless Combustion

The stability of combustion wave propagation is an important factor in determining the quality of materials produced by CS. To produce uniform product, a stable combustion regime is desired. Furthermore, it is also important to know the boundaries where combustion, stable or unstable, can propagate. 

From classic combustion theory (Zeldovich et ai, 1985), the following two conditions must be satisfied for a constant pattern combustion wave with thin reaction zone to be self-propagating  

Numerical results indicate, however, that a condition weaker than Eq. (40) is sufficient to ensure constant-pattern propagation (Aldushin etal, 1978)  

In essence, the preceding conditions require the reaction rate at the combustion temperature, T, to be much greater than that at the initial temperature. To. The ratio of reaction rates at the two temperatures is proportional to 

Puszynski et al. (1987) have suggested the use of the homogeneous explosion criterion for the existence of constant-pattern propagation  

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Steady State Combustion Stability of Gasless Compositions , FizikaGoreniaiVzryva 7, No 3 (1971), 454-57 48) R.L. McKenney, Jr,... 

Linear stability analysis of gasless combustion wave... 

In order to present here some basic results of the weakly stability analysis, we consider below a general reaction-diffusion system of equations. We assume that the problem has a one-dimensional traveling wave solution that loses stability in the same way as the gasless combustion wave as discussed in greater detail below. A study of a general reaction-diffusion system rather than a specific model is useful, because it allows us to focus on general properties of the solution, independent of a particular model. 

We now return to the base model (2,17)-(2.21) of frontal polymerization. We want to find uiuformly propagating FP waves and perform linear and nonlinear stability analyses, as we did in the case of the gasless combustion model. Before we study the model, we would like to reformulate it using the reaction front approximation. 

As was the case with gasless combustion, the uniformly propagating polymerization wave may become unstable as parameters are varied. We perform a linear stability analysis of the uniformly propagating polymerization wave by employing the reaction front approximation. 

Frontal polymerization, the process of propagation of a polymerization wave, is important from both fundamental and applied viewpoints. In this chapter, we reviewed theoretical results on the base model of free-radical frontal polymerization. Based on the analogy of the gasless combustion model and using the methods developed in combustion theory, we determined uniformly propagating polymerization waves and discussed their linear and nonlinear stability. 

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